Electric field
Electric field intensity
Electric potential
Membrane potential
Electric fields organs and tissues
Electrocardiography
Coulomb's Law
• The electric force acting on a point charge q1 as a result
of the presence of a second point charge q2 is given by
F k
q1  q2
r2
where r - distance between charges
ε0 - permittivity of space
Note that this satisfies Newton's third law because it implies
that exactly the same magnitude of force acts on q2 .
Coulomb's law is a vector law and includes the fact that the
force acts along the line joining the charges.
Electric field
• Intensity of an electric field E (or strength of an
electric field or electric field) is vector characteristic.
It is defined as the ratio of the force F acting upon the
test charge to the magnitude of the test charge:
F
E
qtest
Electric field
• The electric field of a point charge can be obtained from
Coulomb's law.
• The magnitude of electric field produced by point charge
Qsource at a distance r from this charge (in a point of M is
where the electric field is defined)
Qsource  qtest
Qsource
F
E
k
k
2
2
qtest
qtest  r
r
Field lines
• An electric field has both magnitude and direction. The
distribution of an electric field in space is visually
represented by the intensity lines (or lines of force or
field lines). Electric field-lines are drawn according to
the following rules:
• The direction of the electric field is everywhere tangent
to the field-lines, in the sense of the arrows on the lines.
The magnitude of the field is proportional to the
number of field-lines per unit area passing through a
small surface normal to the lines.
• The lines of force of a potential electric field
(electrostatic field) that is created by electric charges
originate on positive charges and terminate on negative
charges. The electric field is stronger where the field
lines are close together than where they are farther apart.
Electric field of different charges
Superposition principle of electric field strength
• for a given point in space, the intensity of the field
E, created by several charges, is equal to the vector
sum of the field intensity vectors of the individual
charges:
E  E1  E2  E3  ...
Electric field between two plates charged
by the same density of σ but opposite sign
Electric Dipole
• An electric dipole is a pair of point electric charges
of equal magnitude but opposite sign, separated by
some small distance.
• The distribution of the charge in a dipole can be
characterized by a parameter called the dipole
moment p. The dipole moment is a vector which is
directed from the negative charge towards the
positive charge and is defined as
p  qd
Electric field potential
• The electrostatic force is a potential (conservative) force:
This means that the work it does on a charged particle
depends only on the initial and final position of the particle,
and not on the path followed.
• With each conservative force, a potential energy can be
associated.
• The work done on a charged particle by the potential force
(electric field force) can be represented as a difference of
potential energies of initial and final states.
A  Wp1  Wp 2
Electric field potential
• The electric potential (a scalar quantity) at a point is
equal to the electric potential energy of a charged
particle at that location per unit charge.
Wp

qtest
• The electric potential is independent of the test
particle's charge - it is determined by the electric field
alone.
The potential of electric field of a point charge
If potential 0-level is chosen in infinity The electric
field potential at a point in space is equal to the amount
of work we done by electric force to move the test
charge from the point in question to infinity, divided by
charge. The electric potential created by a point
charge Qsource, at a distance r from the charge (relative
to the potential at infinity), can be shown to be:
Qsource
k
r
Equipotential surfaces
• Points of equal potential form equipotential surfaces
• They exist as a set of non-interlocking surfaces
which are everywhere perpendicular to the direction
of the electric field.
Superposition principle of electric field
potential
• for a given point in space, the total electric
potential, created by several charges, is equal
to the scalar sum of the potentials of the
individual charges:
  1  2  3  ...
The Potential of a Dipole
Sodium‐Potassium Pump
• Each pump cycle consumes one ATP and exchanges
three Na+ for two K+
• Keeps the K+ concentration higher and the Na+
concentration lower with in the cell than in ECF
• Half of daily calories utilized for Na+ ‐ K+
pump
Membrane potential
• Ion transporter (pump proteins)
actively push ions across the
membrane to establish
concentration gradients across the
membrane, and ion channels
allow ions to move across the
membrane down those
concentration gradients.
Differences in concentration of
ions on opposite sides of a
cellular membrane lead to a
voltage called the membrane
potential. For neurons, typical
values of the resting potential
range from –60 to –100 millivolts
Nernst equation for equilibrium potential for
K+ ions.
 
 

RT
K
i  
ln 
zF
K
i
o
• Goldman–Hodgkin–Katz voltage equation
(more commonly known as the Goldman
equation)
 
 

 
 

 
 

RT pK K i  pNa Na i  pCl Cl o
i  
ln



F
pK K o  pNa Na o  pCl Cl i
Action potential
• is a short-lasting event in which the electrical
membrane potential of a cell rapidly rises and
falls, following a consistent trajectory. Action
potentials occur in several types of animal cells,
called excitable cells, which include neurons,
muscle cells, and endocrine cells,
• is generated by special types of voltage-gated
ion channels embedded in a cell's plasma
membrane.
• These channels are shut when the membrane potential is near the
resting potential of the cell, but they rapidly begin to open if the
membrane potential increases to a precisely defined threshold
value. When the channels open, they allow an inward flow of
sodium ions, which changes the electrochemical gradient, which in
turn produces a further rise in the membrane potential. This then
causes more channels to open, producing a greater electric current,
and so on. The process proceeds explosively until all of the
available ion channels are open, resulting in a large upswing in the
membrane potential. The rapid influx of sodium ions causes the
polarity of the plasma membrane to reverse, and the ion channels
then rapidly inactivate. As the sodium channels close, sodium ions
can no longer enter the neuron, and they are actively transported
out of the plasma membrane. Potassium channels are then
activated, and there is an outward current of potassium ions,
returning the electrochemical gradient to the resting state. After an
action potential has occurred, there is a transient negative shift,
called the afterhyperpolarization or refractory period, due to
additional potassium currents. This is the mechanism that prevents
an action potential from traveling back the way it just came.
Propagation
• The action potential generated at the axon
hillock propagates as a wave along the
axon. The currents flowing inwards at a
point on the axon during an action
potential spread out along the axon, and
depolarize the adjacent sections of its
membrane. If sufficiently strong, this
depolarization provokes a similar action
potential at the neighboring membrane
patches.
Einthoven's triangle
Vectorcardiography